Yes, it can be done. It make take more than one adapter in sequence to get from the 3/4" hose connection to the 1/4" plastic tube. Any plumbing department in a decent hardware or home-improvement store will likely have them.
The hose connector threads are different from standard American "NPT" pipe threads. You'll need to go from the 3/4" hose thread on the faucet, to 3/4" NPT thread, and from there it may take one or more reducers to get down to a 1/4" compression fitting that the ice maker wants.
Alternatively, there may also be some adapters in the irrigation and sprinkler pipe section, that can go from the 3/4" hose connector to 1/4" tubing using barbed push-on connectors. Something used for drip-irrigation for plants may have the right sizes.